An application of a spectrophotometer using the visible light or infrared light is the measurement of the thickness of a thin film or a thin layer on a substrate. The principle of the spectroscopic thickness measurement is as follows.
When a ray of measurement light having a single wavelength is cast on a thin layer S, as shown in FIG. 11, a part of the light is reflected on the surface (front surface) S1, and the rest enters the layer S. A part of the incoming light is also reflected by the other surface (back surface or boundary with a substrate) S2, go back through the layer S, and go out through the front surface S1. Since the first reflected light and the second reflected light have different path lengths, an interference occurs between them depending on the wavelength of the measurement light and the thickness of the layer S. When a graph is drawn with the wavelength (or wavenumber) of the measurement light as the abscissa and the intensity of the interference light as the ordinate while the wavelength of the measurement light is changed (or scanned), a wavy interference spectrum is obtained. The waveform of the interference spectrum can be represented by a cosine function, and the cycle interval of the cosine function corresponds to the thickness of the layer.
The wavenumber at every crest (peak-top) or trough (valley-bottom) of the interference spectrum is measured automatically or manually, and the cycle interval in the wavenumbers between the crests or between troughs is determined using, for example, the least square error method. Then the thickness is determined using the wavenumber cycle interval and a known refractive index n.
The shape of interference spectrums obtained through spectroscopies is rarely ideal due to various factors. The factors include the wavenumber dependency of the interference efficiency, the wavenumber dependency of the energy distribution of the light source, and various noises arising from the apparatus. In conventional methods, these factors were not taken into account, and it was assumed that the waveform of the interference spectrum is an ideal cosine curve. Thus it was difficult to improve the accuracy of the thickness measurement.
Another problem in conventional methods is that a unique thickness was supposed for a layer. When, however, one desires to apply the method to a chemical mechanical polisher (CMP), it is necessary to measure different thicknesses of a layer deliberately formed to have several different thicknesses. The chemical mechanical polishing operation should be finished using the measured thicknesses. It was difficult by conventional methods to measure such a plurality of thicknesses.